What does the story teach us about kindness?

Among other things, this story teaches us that kindness can come from the most unexpected places. The prime example of this, of course, is Abel Magwitch's acting as Pip's benefactor. When we—and Pip—first meet Magwitch, he's the last man on earth from whom we'd expect to see any kindness. He's an escaped convict, desperate and on the run from a prison barge. When he sees Pip standing there in the graveyard, he starts threatening and intimidating him. There's certainly not much kindness on display here!
However, as the story progresses, and the full picture emerges, it becomes clear that you can't always judge a book by its cover. Yet this is a society which does precisely that, for this is a society obsessed with appearances. That's why it's so hard for Pip to comprehend that it was Magwitch, and not Miss Havisham, who was his generous benefactor all along. But if there's one thing the story teaches us, it's that kindness will always ultimately prevail against the odds.

Kindness is the all-conquering power in Great Expectations. The story begins with an act of kindness on Pip's part, when he helps Magwitch (though, to be honest, Magwitch does terrify the kid first). Later on, Magwitch repays in kind by becoming Pip's benefactor, helping him to rise in station and achieve his dreams of becoming a young gentleman.
Miss Havisham lacks kindness until the very end. She was hurt as a bride-to-be, jilted on her wedding day, so she takes her hurt out on all men and even on poor Estella, warping her from childhood so that she will grow up to be as cold as Miss Havisham herself. In the end, she repents, hoping to stop the misery her actions were intended to inflict upon Pip.
The story shows that kindness is something anyone is capable of, regardless of class. The privileged are not necessarily kinder than the lower class (like Pip and Joe) or even social outcasts (like the convict Magwitch). Kindness makes a person great, more than money, manners, or social standing does.

The basic moral or thesis of Great Expectations is that one act of Christian kindness can change a man's character for the rest of his life. The whole story evolves from what happens in the first three chapters. Pip brings Magwitch a bottle of brandy and a generous assortment of food, consisting of mincemeat, meat-bone, bread, cheese, and pork pie. Pip is acting out of terror, but he also feels pity for this wretched, starving escaped convict.
Pitying his desolation, and watching him as he gradually settled down upon the pie, I made bold to say, "I am glad you enjoy it."
Magwitch is recaptured and transported to Australia, but Pip's act of Christian charity has renewed the embittered man's faith in human nature and given him something to live for. It is because of Pip that Magwitch grows rich through honest labor and enterprise in the far-off land. It is because of Magwitch's gratitude that Pip's life is so miraculously changed. He is able to fulfill his dream of becoming a gentleman--although the fulfillment turns out to be a disappointment. It is not until Chapter 39 that Pip learns the truth about the source of his great expectations. Magwitch visits him in his rooms on a dark and stormy night and tells him:
"Yes, Pip, dear boy. I've made a gentleman on you! It's me wot has done it! I swore that time, sure as ever I earned a guinea, that guinea should go to you. I swore arterwards, sure as ever I spec'lated and got rich, you should get rich. I lived rough, that you should live smooth. I worked hard that you should be above work. What odds, dear boy! Do I tell it fur you to feel a obligation? Not a bit. I tell it, for you to know as that there hunted dunghill dog wot you kep life in, got his head so high that he could make a gentleman--and, Pip, you're him!"
In addition to learning the truth about the source of his money, education, and even higher expectations, Pip learns the greater truth that all gentlemen and ladies owe their fine clothes, rich foods, polished manners, and inflated egos to the dunghill dogs of the world who labor and suffer to make them the meretricious and feckless parasites most of them are.
The moral or thesis that one act of Christian kindness can change a man's character for the rest of his life is also the guiding force in Victor Hugo's great novel Les Miserables. Hugo's Jean Valjean is in danger of being taken back to the galleys for stealing Bishop Bienvenu's silverware, but the saintly Bishop creates a transformation in Valjean's character by telling the arresting officers that the silver was a gift and even adding a pair of silver candlesticks to the bounty. Jean Valjean becomes an industrious, generous man who devotes the rest of his life to bringing happiness to others.
Great Expectations was published in 1860 and Les Miserables in 1862, but neither author was indebted to the other for his thesis. Rather, both men were inspired by the teachings of Jesus and his followers recorded in the New Testament.